Problem: Graph this system of equations and solve. $-2x-5y = 5$ $2x-5y = -15$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $-2x-5y = 5$ , to slope-intercept form. $y = -\dfrac{2}{5} x - 1$ The y-intercept for the first equation is $-1$ , so the first line must pass through the point $(0, -1)$ The slope for the first equation is $-\dfrac{2}{5}$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move down (because it's negative) You must also move $5$ positions to the right. $5$ positions to the right. $2$ positions down from $(0, -1)$ is $(5, -3)$ Graph the blue line so it passes through $(0, -1)$ and $(5, -3)$ Convert the second equation, $2x-5y = -15$ , to slope-intercept form. $y = \dfrac{2}{5} x + 3$ The y-intercept for the second equation is $3$ , so the second line must pass through the point $(0, 3)$ The slope for the second equation is $\dfrac{2}{5}$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move up You must also move $5$ positions to the right. $5$ positions to the right. $2$ positions up from $(0, 3)$ is $(5, 5)$ Graph the green line so it passes through $(0, 3)$ and $(5, 5)$ The solution is the point where the two lines intersect. The lines intersect at $(-5, 1)$.